Pith Number

pith:J53DQLN7

pith:2010:J53DQLN7GMJYOADZGK4DJ3U5UR

not attested not anchored not stored refs pending

Upper continuity bounds on the relative $q$-entropy for $q>1$

Alexey E. Rastegin

arxiv:1010.1335 v3 · 2010-10-07 · math-ph · math.MP · quant-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J53DQLN7GMJYOADZGK4DJ3U5UR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T04:19:22.034826Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f76382dbf331387007932b834ee9da446c1f16166966ab52675e97e76555a4d

Aliases

arxiv: 1010.1335 · arxiv_version: 1010.1335v3 · doi: 10.48550/arxiv.1010.1335 · pith_short_12: J53DQLN7GMJY · pith_short_16: J53DQLN7GMJYOADZ · pith_short_8: J53DQLN7

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/J53DQLN7GMJYOADZGK4DJ3U5UR \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 4f76382dbf331387007932b834ee9da446c1f16166966ab52675e97e76555a4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac81604204ea58656637b1d1db943740e1701e9048f6268fe1f60f50595f3aca",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-10-07T04:37:00Z",
    "title_canon_sha256": "94830a7fe403e1f2ba1e0027c369f825edf3a71318bf4c09fedb304d2c1cb592"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.1335",
    "kind": "arxiv",
    "version": 3
  }
}